## New NBA stat: Opponent-Adjusted Rating ("OAR")

 Green Stats:

We're introducing a new team-level statistic here today: the Opponent-Adjusted Rating ("OAR") — which takes each each game's Offensive and Defensive Rating and adjusts it to account for opponent strength. This stat is used for gauging a team's true offensive and defensive efficiencies, and for finding trends that are otherwise hard to see.

For each game, we generate an "Offensive OAR" and a "Defensive OAR." We also look at the season's trends for both these stats, as well as the "Net OAR" for each game and the NetOAR running average. (NetOAR is derived by subtracting DefOAR from OffOAR, just like standard Net Ratings.)

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### Opponent Adjusted Ratings ("OAR") — Complete Formulas

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DEFINITIONS:
• OffRtg = Celtics' Offensive Rating for a given game
• OppSeasDefRtg = Opponent's current average Defensive Rating for the season
• OppGameDefRtg = Opponent's Defensive Rating for the given game [Note: this is always equal to the Cs' Offensive Rating (OffRtg) for that game.]
• DefRtg = Celtics' Defensive Rating for the given game
• OppSeasOffRtg = Opponent's current average Offensive Rating for the season
• OppGameOffRtg = Opponent's Offensive Rating for the given game [Note: this is always equal to the Cs' Defensive Rating (DefRtg) for that game.]

FORMULA for the Cs' Opponent Adjusted Offensive Rating ("OffOAR") for a given game:
• OffOAR = OffRtg * (1 - {[OppSeasDefRtg - OppGameDefRtg] / [OppSeasDefRtg]})

FORMULA for the Cs' Opponent Adjusted Defensive Rating ("DefOAR") for a given game:
• DefOAR = DefRtg * (1 - {[OppSeasOffRtg - OppGameOffRtg] / [OppSeasOffRtg]})

FORMULA for NetOAR (as with other "net" stats, it's a simple subtraction):
• NetOAR = OffOAR - DefOAR

WHAT DO THESE RATINGS TELL US?
• The Offensive and Defensive Opponent-Adjusted Ratings (OARs) tell us how much better, or worse, the Cs performed in a given game, on offense and defense, relative to how they were expected to perform based on their opponent's season's ratings for offense and defense.
• This is useful because it solves a long-standing problem with simple Offensive and Defensive Ratings. Here's an example: If the Cs play an offensively-weak team (like PHI) and hold them to a scoring rate equivalent to, say, the #24 team in the NBA, observers could conclude that the Cs' defense performed quite well. And yet, when we check Philly's stats, we see that their season's Offensive Rating is actually the worst in the league: #30. By letting them score at a rate equivalent to #24 in the league, the Celtics' defense actually performed relatively POORLY. Not "well" at all. But that information isn't available when looking solely at the standard ratings for a game.

The OAR stat solves this problem. In the example above, the Defensive OAR ("DefOAR") for the Cs in the (hypothetical) Philly game would be significantly worse than their regular DefRtg — a direct result of the OAR formulas — reflecting the fact that PHI actually scored better than they usually do, better than expected, in the game. It's very useful to have a single-number per-possession stat which reflects offensive or defensive performance that's WEIGHTED by the quality of the opposition.
• NetOAR is derived by subtracting the Defensive OAR from the Offensive OAR (just like standard Net Ratings). It gives us a measure of how much better than expected, or worse, the Cs' overall performance (offense and defense combined) was in a given game. When NetOAR is positive, the Cs performed better than expected in that game, overall; when it's negative, they performed worse than expected.
• And of course, we also do a full season's average of NetOAR (the "Running NetOAR" aka "RunNetOAR"). This gives us an indication of how much better than expected, or worse, the Cs have performed, on average, in the entire season to date.
• Finally, it will be interesting to do a 10-game moving average of the Cs' NetOAR. That would give us a smoothed-out graphical representation of the trend of the Cs' overall competitive performance level. Moving averages are useful for reducing the impact of short term (often single-game) aberrations, aka "outliers." (But we haven't done them yet, in part because there haven't been sufficient games played in the season yet.)
• Note: Obviously, these stats can be used for any team by simply changing "Celtics" references to "Home Team."

CELTICS' CURRENT OARs:
• For the season to date, the Cs' Offensive Opponent-Adjusted Rating ("RunOffOAR") is 104.2 — which correlates to ~#11 in the league in the NBA table of Offensive Efficiency Ratings. This rating is significantly higher than the Celtics' standard OffRtg (indicating that the offense has on average performed better than expected) and it's been rising fairly steadily over the last 3-4 games (indicating the offense is getting better). The last four game OffOARs are: ATL 121.9, OKC 109.0, HOU 109.9, DAL 108.4.
• For the season to date, the Cs' Defensive Opponent-Adjusted Rating ("RunDefOAR") is 92.8 — much lower (and therefore better) than their standard Defensive Efficiency Rating (Def.Rtg.) (97.9) — and correlating to #1 in the league in the NBA table of Defensive Efficiency Ratings. This indicates that the defense is performing much better than average, regularly beating expectations. I.e., "elite." Note: The last four games' DefOARs (90.0, 72.7, 86.0, 118.7) shows us that the Cs' D has been improving, but performed much worse than usual in the DAL game.
• The Cs' Running Net Opponent-Adjusted Rating (RunNetOAR) currently = +11.4 for the season, and is generally trending upward — indicating that the Celtics are performing very well overall, better than expected, and have been trending positive (improving over time) — until the Dallas game, which was a small downward turn.
• Below are three graphs: The first shows the Cs' Running Average Net OARs as it changed after each game (after PHI game #1); the second is a graph of the raw Net OARs (not a running average), and the third uses standard Net Ratings per game instead. The (green) trendline is positive in all three graphs.
• The raw Net Oars will show changes in the team's performance levels first, because there's no running average to create lag.
• The graph of the running average Net OARs is the smoothest, as expected — but also the one with the greatest lag behind any new changes to team performance that may develop over time.
• The Net Ratings graph is shown for comparison with the OARs graphs.
• OARs are much more sensitive than simple Net Ratings to team performance relative to opponent strength. The shapes of the graphs for Net Ratings and Net OARs are similar, but the values at each point can vary substantially, depending on the relative strength or weakness of each opponent.
• As the season moves on, we can expect the OARs to show us certain movements in the team's performance levels well in advance of any clear changes in the standard measures currently in use.

Note: When we have some more data to work with, we may add a graph of the 5-game and/or 10-game NetOAR moving average — just for kicks.

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Please feel free to comment and/or dissect and/or throw tomatoes at anything in this post, in the comment section below.

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Green Stats runs an analysis of each Celtics game, usually within ~ 1 to 20 hours after the final horn.
Note: Some posts will be (much) longer than others.

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Efficiency ratings source for comps: Basketball-reference.com

Connect with DRJ on Twitter @DRJ_CsNStats

DRJ
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